The Exponential Stability Of One-dimensional Nonlinear Stochastic Differential Equation

Recently, the stability of the stochastic system has been attracting more and more attention of the probability theory scholars and practical application sta?, meanwhile has given birth to many research results. In general, most of the predecessors’ results start from the generator of the system and take Lyapunov method as the main tool, thus obtaining the stability criterion of the system. This paper starts from the transformation of stochastic differential equations, locally transform stochastic di?erential equations into ordinary differential equations with random terms. Thus the exponential stability condition of the system is obtained. Our condition is more practical on account of the fact that it needs only the derivative of the stochastic system in the equilibrium point.